CP for Sudoku Study & compare the effectiveness of constraint propagation algorithms

1. Using Constraint Processing to Model, Solve & Support the Interactive Solving of Sudoku Puzzles Christopher G. Reeson & Berthe Y. Choueiry •Constraint Systems Laboratory • University of Nebraska-Lincoln Solver: sudoku.unl.edu/Solver•Constructor: sudoku.unl.edu/Constructor Goals Implementation Constraint Propagation Solver is a Java applet that uses CP techniques to support the user to play Sudoku. The player can… • CP for Sudoku • Study & compare the effectiveness of constraint propagation algorithms • CP for computer-human interaction • Guide & train human players • Sudoku to illustrate & teach CP • … Deconstructing Sudoku • Demystify the puzzle • Discourage students from losing time playing it …undo/redo any action …load an instance from the online library …assign all cells whose domains have a single value …assign values to cells and play the game without aid FC …check the number of solutions left Sudoku AC A Sudoku… …display the remaining values in the domain of each cell …apply a variety of CP techniques • is well posed if it has a single solution • is minimal if removing any ‘given’ yields more than one solution • is symmetric if the filled cells on the grid exhibit some axial symmetry GAC Solver detects errors and highlights the variables in the broken constraint Solver displays the number of hints. The user can iterate through them. The user can choose the type of hint & the level of consistency: SAC Hint highlights the cell to think about.. SGAC • 2 types of hints: Singleton & Vital • 8 levels: FC, AC, Single GAC, GAC, Single SAC, SAC, Single SGAC, SGAC #15 on Royle’s web site1 CSP Model Impact Each cell is a variable whose domain is set of numbers 1…9. The constraints are ‘all-different’ constraints on each row, column, and block. Inspired a PhD student @ USC to use propagation for constraint model generation from data We can model each all-diff constraint as either a set of binary mutex constraints... …or single non-binary alldiff constraints with arity 9. By Angelo Kai-Chen Huang @ USC • Constructor • Collaboration with an MS student @ USC • Supports entering & storing instances • Counts & displays all solutions • Will support generalization to other Sudoku variations • Conjectures: • SGAC  relation (1,2)consistency • SGAC can solve a well posed 9x9 Sudoku Implementing both models allows the player to compare and understand the effectiveness of constraint propagation operating on each model. References Support: UCARE grant awarded to Chris Reeson & CAREER Award #0133568 from the National Science Foundation. • Gordon Royle. Minimum Sudoku. people.csse.uwa.edu.au/gordon/sudokumin.php, 2005 • Helmut Simonis. Sudoku as a Constraint Problem. Workshop on Modeling and Refomulating CSPs, 2005